[ (x^2+y^2-2x-4y-4)\cdot 8 = (4x+y-2)^2 . ]
The book "Analytical Geometry" by PN Chatterjee is a comprehensive textbook that covers the fundamental concepts of analytical geometry. The book provides a detailed and systematic treatment of the subject, making it an ideal resource for students and teachers alike. The book covers a wide range of topics, including: analytical geometry pn chatterjee pdf link
It doesn't skip steps in derivations, making it great for self-study. Exam Alignment: 📚 Analytical Geometry – P
| Part | Chapter | Core Topics Covered | Typical Applications | |------|---------|---------------------|----------------------| | | 1. Straight Lines | Slope, intercept form, general form, distance of a point, angle between lines, family of lines, concurrency | Coordinate geometry of linear equations, engineering drawings | | II | 2. Circles | Standard & general equation, tangent, chord, power of a point, coaxial circles, inversion | Design of gears, circular motion, optics | | III | 3. Conic Sections – Parabola | Focus‑directrix definition, standard & general forms, tangent, normal, chord of contact, reflective property | Projectile motion, satellite dish design | | IV | 4. Conic Sections – Ellipse | Standard & general equation, eccentricity, focal properties, tangents, normals, polar coordinates | Planetary orbits, elliptical mirrors | | V | 5. Conic Sections – Hyperbola | Standard & general form, asymptotes, transverse & conjugate axes, rectangular hyperbola, rectangular coordinates transformation | Relativistic motion, navigation systems | | VI | 6. Pair of Straight Lines & Their Geometry | Joint equation, angle between lines, combined equations, concurrency, polar lines | Structural analysis, circuit diagrams | | VII | 7. General Second‑Degree Curves | Classification via discriminant, rotation of axes, translation of axes, canonical forms | Advanced CAD, robotics path planning | | VIII | 8. Three‑Dimensional Geometry | Direction cosines, plane equations, line–plane relationships, distance formulae, quadric surfaces (ellipsoid, hyperboloid, paraboloid) | 3‑D modeling, aerospace engineering | | IX | 9. Spherical & Cylindrical Coordinates | Transformations, equations of surfaces, applications to physics | Fluid dynamics, electromagnetic field problems | | X | 10. Miscellaneous Topics | Loci, locus of points, loci of circles, pedal curves, envelopes | Problem‑solving tricks, Olympiad‑style geometry | The book covers a wide range of topics,